Peridynamic formulations for planar arbitrarily curved beams with Euler-Bernoulli beam model

Abstract

This study presents two peridynamic formulations for analysis of planar arbitrarily curved beams using kinematic assumptions of Euler-Bernoulli beam model. Only displacement components of the beam axis are considered as kinematic unknowns. The principle of virtual work is used to derive equilibrium equations and boundary conditions. The equilibrium equations are presented in two forms, i.e., one in terms of cross-sectional stress resultants and one in terms of displacement components of the beam axis. Then, two peridynamic formulations are developed respectively from two forms of equilibrium equations by employing peridynamic functions, which are constructed with the concept of peridynamic differential operators. Several examples are presented to elucidate the performance of the proposed formulations in some regards, i.e., numerical precision, convergence properties, and robustness with respect to the membrane locking effect.